CAJ | 학술논문

本文是对2013年全国大学生数学建模竞赛A题的解答。通过参考国家标准的道路通行能力评价体系，建立了准确求解道路在发生交通事故后的实际通行能力的数学模型；同时，基于交通流二流理论建立了排队长度分析模型，评估其与各影响因素之间的关系。在问题1中，以红绿灯导致的车流量周期性变化规律为依据，引入相关修正系数对模型进行修正，得出求解实际通行能力的模型。在问题2中，对统计数据进行加权平均后计算出道路的实际通行能力，再对比所堵车道的车流量，分析得车道车流量与通行能力的关系。在问题3中，根据交通流二流理论和流量稳定方程建立排队长度的分析模型，再运用控制变量法和MATLAB制图定性分析车辆排队长度与事故断面实际通行能力、事故持续时间和路段上游车辆数间的灵敏度。在问题4中，利用问题3建立的当量排队模型进行适当推导，即得排队长度达到140 m的时间估算模型。
본문시대2013년전국대학생수학건모경새A제적해답。통과삼고국가표준적도로통행능력평개체계，건립료준학구해도로재발생교통사고후적실제통행능력적수학모형；동시，기우교통류이류이론건립료배대장도분석모형，평고기여각영향인소지간적관계。재문제1중，이홍록등도치적차류량주기성변화규률위의거，인입상관수정계수대모형진행수정，득출구해실제통행능력적모형。재문제2중，대통계수거진행가권평균후계산출도로적실제통행능력，재대비소도차도적차류량，분석득차도차류량여통행능력적관계。재문제3중，근거교통류이류이론화류량은정방정건립배대장도적분석모형，재운용공제변량법화MATLAB제도정성분석차량배대장도여사고단면실제통행능력、사고지속시간화로단상유차량수간적령민도。재문제4중，이용문제3건립적당량배대모형진행괄당추도，즉득배대장도체도140 m적시간고산모형。
In this paper, a solution is presented for the Problem A of Contemporary Undergraduate Mathematical Contest in Modeling in 2013. A model was built for calculating the passing capacity of city roads after traffic accidents,with reference to the traffic capacity of the national standard evaluation system. Meanwhile, a model of queuing length was built to figure out the relation between factors from the traffic flow second-rate theory. Based on cyclic variation of traffic flow and by adding correction factors, a model for calculating actual passing capacity was built in Question 1. In Question 2, the relation between traffic flow and passing capacity was figured out by taking a weighted average of the actual passing capacity of the road and comparing the traffic flow at different times. A model was built to evaluate the effect of queuing length, incident duration and the amount of vehicles on the upstream section to actual passing capacity during traffic accidents,according to the traffic flow second-rate theory and flow stability equation. In Question 4, the time when the queuing length is 140 meters was figured out via using the model of Question 3.